Drivers of the US CO2 emissions 1997–2013

Fossil fuel CO2 emissions in the United States decreased by ∼11% between 2007 and 2013, from 6,023 to 5,377 Mt. This decline has been widely attributed to a shift from the use of coal to natural gas in US electricity production. However, the factors driving the decline have not been quantitatively evaluated; the role of natural gas in the decline therefore remains speculative. Here we analyse the factors affecting US emissions from 1997 to 2013. Before 2007, rising emissions were primarily driven by economic growth. After 2007, decreasing emissions were largely a result of economic recession with changes in fuel mix (for example, substitution of natural gas for coal) playing a comparatively minor role. Energy–climate policies may, therefore, be necessary to lock-in the recent emissions reductions and drive further decarbonization of the energy system as the US economy recovers and grows.


Supplementary Table 1
Subscript for the components in the coefficients Weight K first second third fourth fifth 0

Supplementary Methods
As presented in Methods section in the main text, in this study the change of CO 2 emission is decomposed into six additive terms, and each term represents the contribution of the changing factor to the total change of CO 2 emission in the US. One can perceive a logical pattern that the changing factors is placed, at each term, in turn from left to right in the product with all other factors; and the other unchanged factors on the left hand side of the changing factors are in base year value (year "t  1"); and the ones on the right hand side of the changing factors are in target year value (year "t"). Therefore, by extracting the unchanged values in each term the equation can be merged as: (1) where the , , , , , and are the so-called "weight" or "coefficient" for each "Δfactor" respectively. The calculation of these "weights" or "coefficients" are usually done via econometric methods; alternatively, they can be generated via a more straight forward way by deriving them with the structural decomposition method 7, 8 .
However, supplementary equation (1) is not a unique decomposition equation, which is only one of the 720 decomposition equations by assuming the order of the driving forces of "p·f·E·L·y s ·y v ". However, the order can also be "f·p·E·L·y s ·y v " or "f·E·p·L·y s ·y v " and so on.
Although each decomposition equation would produce exactly the same result for ΔCO 2 , de Haan 9 found that the size of the contribution of each "Δfactor" significantly differs across the equations.
In other words, the "coefficient" (w) of each "Δfactor" is varied in different equations.
Due to the non-uniqueness issue, Dietzenbacher and Los 10 suggested to take the average of all the n! (6! in this case) decomposition equations (Supplementary Table 1). In order to do so, all the 720 equations need to be sorted into a standard order, for example, every term in the equation needs to be re-arranged to the order of "p·f·E·L·y s ·y v ", and the "Δfactor" is in turn placed from the first factor of "p" in the first term of the equation to the last factor of y s in the last (seventh) term.
Then, all the equations have been re-arranged in the same pattern. For example, the first term of every equation contains the information of the contribution of population growth (Δp) to the change of CO 2 (ΔCO 2 ) with other factors kept unchanged. The product of the unchanged values of other factors is the "coefficient" for Δp. The "coefficient" appears 120 times, and same as the "coefficient" does. de Haan 9 and Seibel 11 found that each term in the equation always has 2 (n-1) different "coefficients" attached to the "Δfactor", 2 (6-1) = 32 different "coefficients" to every "Δfactor" in this case.
Next one can calculate the "weights" of the "coefficients" which is attached to the "Δfactor".
The easiest way is via observations, to count how many cases of "Δfactor" are attached to the same "coefficient". For example as mentioned previously, the "coefficient" appears 120 times in the 720 equations, and therefore its weight is 120. However, the observation method could be difficult in large number of decomposition equations with more than 5 factors.
Seibel 11 proposed a mathematic method to deal with this. Firstly, let k represent the number of subscript "t  1" (base year) in a coefficient; k runs from "0" to "n  1"; therefore, the number of subscript "t" (target year) would be "n  1  k". Secondly, for each k, the number of different coefficients attached to the "Δfactor" can be calculated by: In this study, n is set to 6 (six factors). So when k = 0 or 5, there is only one coefficient for each case; when k = 1 or 4, the number of different coefficients are 5 respectively; when k = 2 or 3, there would be 10 different coefficients. Thirdly, supplementary equation (3) calculates how many times each of these coefficients is repeated as "weights" for each "Δfactor" term in every equation and it is similar to obtain other "w"s in supplementary equation (1).